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As noted above,, that serial number shows the gun was made in 1961.
To be 100% sure of the chambering,, get a .22 magnum round,, and see if it will fit in the cylinder. If it does,, it's a magnum. A .22 LR will also fit,, AND shoot through it. But the cases will often split,, and get stuck a bit in the chambers.
Ruger can fit a new cylinder,, but they will also do a mandatory "safety transfer bar" upgrade. Most of the time,, they do return the OM parts,, but many folks prefer to NOT send them in a gun for any work to assure they get the original parts back.
As noted,, you can easily find a spare cylinder on many places like ebay, or gunbroker or even in our classifieds here. To post an ad here,, you'll need to have at least 10 posts before allowed that privilege.
The very good news is that getting a different cylinder for those guns is pretty easy,, AND you normally never have to worry about "timing." the only thing you need to do is find a cylinder,, that has the Over All Length, (OAL) the same as your current cylinder. Measure your cylinder from the very front of the cylinder pin boss to the very rear of the ratchet. That's your OAL. Look for one that's the same or a few thousands longer. A longer one can be easily honed down (the boss area,) to fit. I always purchase spare cylinders for Rugers anytime I find a good deal. I put them in my spare cylinder box,, and when I find a gun that's supposed to be a convertible,, but missing the spare,, I go to digging in my stuff. I've never had an odd spare NOT time correctly.
And it's much cheaper to get a spare off these places than having Ruger build one.
